The deployment of Aerial Base Stations (ABSs) mounted on board Unmanned Aerial Vehicles (UAVs) is emerging as a promising technology to provide connectivity in areas where terrestrial infrastructure is insufficient or absent. This may occur for example in remote areas, large events, emergency situations, or areas affected by a natural disaster such as a wildfire or a tsunami. To successfully materialize this goal, it is required that ABSs are placed at locations in 3D space that ensure a high Quality of Service (QoS) to the ground terminals. This paper provides a tutorial introduction to this ABS placement problem where the fundamental challenges and trade-offs are first investigated by means of a toy application example. Next, the different approaches in the literature to address the aforementioned challenges in both 2D or 3D space will be introduced and a discussion on adaptive placement will be provided. The paper is concluded by discussing future research directions.